Model description—NSSA

When determining the stresses, present in a weld spot, you have to consider the following important topics. Although every spot weld of a component can be created under equal manufacturing conditions the shape of the notch between the connected sheet metals may vary from spot weld to spot weld. When the weld diameter is big enough (), the crack will not occur at the sharp edges of the weld nugget but further ahead in the sheet metal. The generation of the cracks is also material and load dependent. Next to that, you have to consider that relevant plastic deformation can also occur locally at locations that are below the fatigue limit. Based on these three reasons it is stated in [3] that: "an exact stress calculation is difficult to perform by applying a notch-root analysis or fracture mechanics because the true conditions at the spot weld are not reflected by these theories". These computations are also very time consuming and hardly realistic.

In the following figure, shell elements are used for the sheet metal representation, while the spot weld nugget is modeled using beam elements.

Representation of a Spot Weld Based on Rupp's Approach

Nowadays, it has almost become a standard to calculate the stresses of complex spot welded structures by using so-called general structural models. In these finite element models the sheet metal components are modeled using shell-elements, while the spot weld nugget is often modeled using a beam-element or solid-element (as shown in the figure above). Such a representation results in a simplified spot weld model that can only provide the sectional forces and moments, which are transmitted by each spot weld joint. There is no information available about the local stress conditions around the nugget which influence the crack generation and propagation. As it is stated in [3], this method is still capable of calculating the local stresses based on the cross-sectional forces and moments, which result from the general structural calculations. The method was validated by comparing the calculated stresses of fine mesh models with experimentally determined stresses. In a second step, the results from the fine mesh models were used to develop a coarser mesh model for which the results were compared with those from the fine mesh models. [3]. These coarse mesh models were capable of generating realistic results if the following conditions were met:

• The one-dimensional beam-elements should be very stiff in comparison to the sheet metal. This should also be the case when solid elements are used.

• The dimensioning of a sheet-element next to weld-spot elements should be twice the weld spot diameter.

• The support effect of two sheet metals, connected by the spot weld, is not considered.

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